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13.Statistics
medium
If for a distribution $\Sigma(x-5)=3, \Sigma(x-5)^{2}=43$ and the total number of item is $18,$ find the mean and standard deviation.
Option A
Option B
Option C
Option D
Solution
Given, $n=18, \Sigma(x-5)=3$ and $\Sigma(x-5)^{2}=43$
$\therefore \quad \operatorname{Mean}=A+\frac{\Sigma(x-5)}{18}=5+\frac{3}{18}=5+0.1666=5.1666=5.17$
and $\quad SD =\sqrt{\frac{\Sigma(x-5)^{2}}{n}-\left(\frac{\Sigma(x-5)}{n}\right)^{2}}=\sqrt{\frac{43}{18}-\left(\frac{3}{18}\right)^{2}}$
$=\sqrt{2.3889-(0.166)^{2}}=\sqrt{2.3889-0.0277}=1.53$
Standard 11
Mathematics
Similar Questions
From the data given below state which group is more variable, $A$ or $B$ ?
Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
hard